A Comprehensive Study of Neutrosophic SuperHyper BCI-Semigroups and their Algebraic Significance
محورهای موضوعی : Transactions on Fuzzy Sets and Systems
Ajoy Kanti Das
1
,
Rajat DAS
2
,
Suman Das
3
,
Bijoy Krishna Debnath
4
,
Carlos Granados
5
,
Bimal Shil
6
,
Rakhal Das
7
1 - Department of Mathematics, Tripura University, Agartala, India.
2 - Department of Mathematics, Tripura University, Agartala,Tripura, India.
3 - Department of Education (ITEP), NIT Agartala, Agartala,Tripura, India.
4 - Department of Applied Sciences, School of Engineering, Tezpur University, Assam, India.
5 - Department of Mathematics, Universidad de Antioquia, Medellin, Colombia.
6 - Department of Statistics, Tripura University, Agartala, India.
7 - Department of Mathematics, The ICFAI University Tripura, Agartala, India.
کلید واژه: Neutrosophic, SuperHyperStructure, SuperHyperAlgebra, SuperHyper Operations, BCI-Algebras, Semigroups, Ideal.,
چکیده مقاله :
This paper introduces and explores the concept of neutrosophic superhyper BCI-semigroups, an advanced algebraic structure integrating neutrosophic logic, superhyper operations, and BCI-algebras into a semigroup framework. Neutrosophic superhyper BCI-semigroups facilitate the handling of indeterminate and conflicting information by incorporating neutrosophic triplets for each element, denoting degrees of truth, indeterminacy, and falsity. The study defines essential properties such as closure, associativity, BCI identity, and neutrosophic membership and provides illustrative examples to demonstrate these properties in practical scenarios. Further, the paper delves into the characteristics of idempotent and commutative elements, homomorphisms, ideals, subsemigroups, and quotient sets within the context of neutrosophic superhyper BCI-semigroups. Key theorems are presented to establish foundational principles and behaviors of these structures, highlighting their theoretical implications and potential for practical applications.
This paper introduces and explores the concept of neutrosophic superhyper BCI-semigroups, an advanced algebraic structure integrating neutrosophic logic, superhyper operations, and BCI-algebras into a semigroup framework. Neutrosophic superhyper BCI-semigroups facilitate the handling of indeterminate and conflicting information by incorporating neutrosophic triplets for each element, denoting degrees of truth, indeterminacy, and falsity. The study defines essential properties such as closure, associativity, BCI identity, and neutrosophic membership and provides illustrative examples to demonstrate these properties in practical scenarios. Further, the paper delves into the characteristics of idempotent and commutative elements, homomorphisms, ideals, subsemigroups, and quotient sets within the context of neutrosophic superhyper BCI-semigroups. Key theorems are presented to establish foundational principles and behaviors of these structures, highlighting their theoretical implications and potential for practical applications.
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